The report claims the Russian side have sent scouts to recent Benfica matches to watch Gaitan and teammate Ezequiel Garay in action.
Liverpool and Manchester United have also been strongly linked with the Argentina playmaker, but Benfica and Zenit's close dealings in recent transfer windows gives them the edge.
As part of the negotiations that brought Belgian international Axel Witsel to Russia in 2012 for €40m, the two clubs reportedly agreed to an informal arrangement whereby Benfica would keep Zenit up to date on offers for Gaitan from rival suitors.
A similar set-up was arranged for Garay, but as the report notes the final decision over any move remains up to the player.
The Benfica defender had the chance to join Zenit before the close of the Russian transfer window last month, but turned down a bigger wage in Russia to give himself the best chance of making Argentina's World Cup squad.
United's interest in Gaitan dates back to the Sir Alex Ferguson era, when the Old Trafford manager's brother, Martin Ferguson, gave the Argentinian a glowing scouting report.
Most recently, Liverpool boss Brendan Rodgers has been mentioned as a potential suitor, with a summer offer potentially on the cards after failed Anfield moves for Yevhen Konoplyanka, Willian and Mohamed Salah in recent windows.